The generator matrix

 1  0  0  0  1  1  1  1  2  1  X  1 X+2  1  2  X  X  2  1  0  1  2  1  1  X  1  1  1  X  1 X+2  0  1  X  1  1  1  0  1  1  1
 0  1  0  0  0  1  2  3  1 X+2  0 X+1  1  1  1  1  1  2  0  0 X+2 X+2  3 X+3 X+2 X+3  X  X  1 X+2  2  1 X+2  2  2 X+3 X+1  1 X+1  2  1
 0  0  1  0  0  1  3  2  3  1  1  3  X X+2  1  X  2  1 X+3  1  1  0 X+3  X  1 X+2 X+1  3  X  2  1  1 X+3 X+2  0 X+1  0 X+2 X+3 X+2 X+3
 0  0  0  1  1  2  1  3  3  0 X+3  3 X+3 X+2  X  1  0  X  3  1 X+2  1 X+3 X+2 X+3  0 X+1  X  1 X+2  0 X+1  1  1  3 X+1  X  X  2 X+3  0
 0  0  0  0  X  0  0  0  0 X+2  X  X  X X+2 X+2  X  2  2  2 X+2  X  2  X  2  2  2 X+2  2  2 X+2  X  X  X  X  2  2 X+2  0  0  2  2

generates a code of length 41 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+135x^34+462x^35+831x^36+1082x^37+1346x^38+1584x^39+1753x^40+1904x^41+1837x^42+1730x^43+1449x^44+978x^45+631x^46+380x^47+154x^48+60x^49+48x^50+4x^51+4x^52+8x^53+3x^54

The gray image is a code over GF(2) with n=164, k=14 and d=68.
This code was found by Heurico 1.13 in 2.45 seconds.